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mitted a show of petulance when the mouth he tries to feed bites
him. Nevertheless Jacobi's desperate plight was enough to
excite anybody's sympathy. Married and practically penniless
he had seven small children to support in addition to his wife.
A Mend in Gotha took in the wife and children, while Jacobi
retired to a dingy hotel room to continue his researches.
He was now (1849) in his forty-fifth year and, except for
Gauss, the most famous mathematician in Europe. Hearing of
his plight, the University of Vienna began angling for him. As
an item of interest here, Littrow, Abel's Viennese friend, took
a leading part hi the negotiations. At last, when a definite and
generous offer was tendered, Alexander von Humboldt talked
the sulky King round; the allowance was restored, and Jacobi
was not permitted to rob Germany of her second greatest man.
He remained in Berlin, once more in favour but definitely out
of politics.
The subject, elliptic functions, in which Jacobi did his first
great work, has already been given what may seem like its
5-hare of space; for after all it is to-day more or less of a detail in
the vaster theory of functions of a complex variable which, in
its turn, is fading from the ever changing scene as a thing of
living interest. As the theory of elliptic functions will be men-
tioned several times hi succeeding chapters we shall attempt a
brief justification of its apparently unmerited prominence.
No mathematician would dispute the claim of the theory of
functions of a complex variable to have been one of the major
fields of nineteenth-century mathematics. One of the reasons
why this theory was of such importance may be repeated here.
Gauss had shown that complex numbers are both necessary and
sufficient to provide every algebraic equation with a root. Are
any further, more general, kinds of 'numbers' possible? How
might such 'numbers' arise?
Instead of regarding complex numbers as having first pre-
sented themselves hi the attempt to solve certain simple
equations, say a* + 1  0, we may also see their origin in
another problem of elementary algebra, that of factorization.
To resolve **  y* into factors of the first degree we need
nothing more mysterious than the positive and negative